Finite Group Databasebeta

← C13×#19033 #15705372

Subgroups — C13×#19033 #15705372

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic, complemented
3C13×#3165C211yesmaximal, characteristic, complemented
4C2×C13×#497C211yesmaximal, characteristic, complemented
5C13×#1661C214yesmaximal, complemented
6C13×#1660C214yesmaximal, complemented
7C13×#1531C211yesmaximal, characteristic, complemented
8C13×#1527C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C22×C13×Q16—21no—
11C22×C13×SD16—21no—
12C13×#563C2212yes—
13C13×#562C2212yes—
14C13×#556—21no—
15C13×#551—22no—
16D4×Q8×C13—21no—
17C13×#548—21no—
18C13×#546—21no—
19C13×#543—21no—
20C13×#542—21no—
21C13×#542—22no—
22C13×#538—21no—
23C13×#536—21no—
24C13×#533C2211yescharacteristic
25C2×C13×C4⋊Q8C2211yescharacteristic
26C13×#529C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C13×#501C2214yescomplemented
29C13×#501C2212yescomplemented
30C13×#500—21no—
31C13×#498—21no—
32C13×#497—22no—
33C13×#497C2214yes—
34C13×#489C2212yescomplemented
35C13×#484—21no—
36C13×#481—21no—
37C13×#475—21no—
38C13×#474—21no—
39C13×#432C2211yescharacteristic
40C13×#428—22no—
41C4×C13×M16C2211yescharacteristic
42C2×C13×#97C2211yescharacteristic
43C13×#330C2212yescomplemented
44C13×#330C2214yescomplemented
45C13×#329C2214yes—
46C13×#329C2212yescomplemented
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13D411yescharacteristic
52C2×C13×Q16—24no—
53C2×C13×Q16—44no—
54C2×C13×SD16—24no—
55C2×C13×SD16—44no—
56C2×C13×M16—21no—
57C22×C8×C13—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—22no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8D411yescharacteristic
64C13×C4⋊Q8D411yescharacteristic
65C13×C4⋊Q8C2312yes—
66C13×#126—22no—
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—21no—
70C13×#125C2311yescharacteristic
71C13×#125C2312yes—
72C13×#124—21no—
73C13×#124—22no—
74C13×#124—22no—
75C13×#124—21no—
76C13×#124—21no—
77C13×#124D412yes—
78C13×#124C2312yes—
79C13×#124C2311yescharacteristic
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—21no—
83C13×#123—22no—
84C13×#123—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8—21no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8D411yescharacteristic
96C13×#121—21no—
97C13×#121—22no—
98C13×#121—22no—
99C13×#121D411yescharacteristic
100C13×#120—22no—
101C4×Q8×C13—21no—
102C4×Q8×C13—21no—
103C4×Q8×C13—21no—
104C4×Q8×C13D411yescharacteristic
105C4×D4×C13—22no—
106C4×D4×C13—21no—
107C4×D4×C13—22no—
108C4×D4×C13—21no—
109C4×D4×C13D411yescharacteristic
110C13×#117—22no—
111C13×#117—21no—
112C13×#117D412yes—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C42×C13C2311yescharacteristic
119C13×#107—24no—
120C13×#107—22no—
121C13×#106—24no—
122C13×#106—22no—
123C13×C4⋊C8—21no—
124C13×#103—22no—
125C13×#102—22no—
126C13×C22⋊C8—21no—
127C13×#97—21no—
128C13×#97C2312yes—
129C13×#97C2312yes—
130C13×#97C2312yes—
131C4×C8×C13—21no—
132#19033C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—21no—
134C13×#41—82no—
135C2×Q8×C13—22no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—22no—
140C2×Q8×C13—42no—
141C2×Q8×C13—42no—
142C2×Q8×C13—42no—
143C2×Q8×C13—41no—
144C2×Q8×C13—82no—
145C2×Q8×C13C2×D411yescharacteristic
146C2×Q8×C13C2×D412yes—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—42no—
152C2×D4×C13C2×D411yescharacteristic
153C2×D4×C13C2×D412yes—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—41no—
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C13×Q16—48no—
164C13×SD16—48no—
165C13×M16—24no—
166C2×C8×C13—24no—
167C2×C8×C13—22no—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4C2×D412yes—
187C13×C4⋊C4C2×D411yescharacteristic
188C13×C4⋊C4C2×D412yes—
189C13×C4⋊C4C2×D411yescharacteristic
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—21no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—21no—
204C13×C22⋊C4—21no—
205C42×C13—22no—
206C42×C13—22no—
207C42×C13—21no—
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2×D411yescharacteristic
211C42×C13C2411yescharacteristic
212#3561C2×C1311yescharacteristic
213#3239C2×C1311yescharacteristic, complemented
214#3165C2×C1311yescharacteristic, complemented
215C2×#497C2×C1311yescharacteristic, complemented
216#1661C2×C1314yescomplemented
217#1660C2×C1314yescomplemented
218#1531C2×C1311yescharacteristic, complemented
219#1527C2×C1311yescharacteristic, complemented
220#1524C2×C1311yescharacteristic, complemented
221C23×C13—22no—
222C23×C13—21no—
223C23×C13—42no—
224C23×C13—81no—
225C23×C13—81no—
226C23×C13#12011yescharacteristic
227Q8×C13—42no—
228Q8×C13—41no—
229Q8×C13—42no—
230Q8×C13—42no—
231Q8×C13—42no—
232Q8×C13—42no—
233Q8×C13—81no—
234Q8×C13—82no—
235Q8×C13—82no—
236D4×C13—42no—
237D4×C13—41no—
238D4×C13—42no—
239D4×C13—42no—
240D4×C13—82no—
241D4×C13—82no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—41no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—81no—
254C2×C4×C13—82no—
255C2×C4×C13—82no—
256C2×C4×C13—82no—
257C2×C4×C13—82no—
258C2×C4×C13#12011yescharacteristic
259C2×C4×C13#12011yescharacteristic
260C2×C4×C13#12011yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C22×D411yescharacteristic
263C2×C4×C13C22×D411yescharacteristic
264C8×C13—24no—
265C8×C13—24no—
266C8×C13—42no—
267C22×Q16—21no—
268C22×SD16—21no—
269#563C22×C1312yes—
270#562C22×C1312yes—
271#556—21no—
272#551—22no—
273D4×Q8—21no—
274#548—21no—
275#546—21no—
276#543—21no—
277#542—21no—
278#542—22no—
279#538—21no—
280#536—21no—
281#533C22×C1311yescharacteristic
282C2×C4⋊Q8C22×C1311yescharacteristic
283#529C22×C1311yescharacteristic
284C2×#124C22×C1311yescharacteristic
285#501C22×C1314yescomplemented
286#501C22×C1312yescomplemented
287#500—21no—
288#498—21no—
289#497—22no—
290#497C22×C1314yes—
291#489C22×C1312yescomplemented
292#484—21no—
293#481—21no—
294#475—21no—
295#474—21no—
296#432C22×C1311yescharacteristic
297#428—22no—
298C4×M16C22×C1311yescharacteristic
299C2×#97C22×C1311yescharacteristic
300#330C22×C1312yescomplemented
301#330C22×C1314yescomplemented
302#329C22×C1314yes—
303#329C22×C1312yescomplemented
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—41no—
307C22×C13—42no—
308C22×C13—41no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—41no—
312C22×C13—162no—
313C22×C13#45612yes—
314C22×C13C2×#12011yescharacteristic
315C4×C13—21no—
316C4×C13—21no—
317C4×C13—21no—
318C4×C13—21no—
319C4×C13—21no—
320C4×C13—41no—
321C4×C13—42no—
322C4×C13—42no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—42no—
326C4×C13—82no—
327C4×C13#45312yes—
328C2×#41—21no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×Q8D4×C1311yescharacteristic
332C22×D4D4×C1311yescharacteristic
333C2×Q16—24no—
334C2×Q16—44no—
335C2×SD16—24no—
336C2×SD16—44no—
337C2×M16—21no—
338C22×C8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—22no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8D4×C1311yescharacteristic
345C4⋊Q8D4×C1311yescharacteristic
346C4⋊Q8C23×C1312yes—
347#126—22no—
348#126—22no—
349#126—22no—
350#126—21no—
351#125C23×C1311yescharacteristic
352#125C23×C1312yes—
353#124—21no—
354#124—22no—
355#124—22no—
356#124—21no—
357#124—21no—
358#124D4×C1312yes—
359#124C23×C1312yes—
360#124C23×C1311yescharacteristic
361#123—22no—
362#123—22no—
363#123—21no—
364#123—22no—
365#123—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—21no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376C22⋊Q8D4×C1311yescharacteristic
377#121—21no—
378#121—22no—
379#121—22no—
380#121D4×C1311yescharacteristic
381#120—22no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8D4×C1311yescharacteristic
386C4×D4—22no—
387C4×D4—21no—
388C4×D4—22no—
389C4×D4—21no—
390C4×D4D4×C1311yescharacteristic
391#117—22no—
392#117—21no—
393#117D4×C1312yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C42C23×C1311yescharacteristic
400#107—24no—
401#107—22no—
402#106—24no—
403#106—22no—
404C4⋊C8—21no—
405#103—22no—
406#102—22no—
407C22⋊C8—21no—
408#97—21no—
409#97C23×C1312yes—
410#97C23×C1312yes—
411#97C23×C1312yes—
412C4×C8—21no—
413C2×C13—22no—
414C2×C13—81no—
415C2×C13—82no—
416C2×C13C2×#45311yescharacteristic
417C2×C13C2×#45611yescharacteristic
418C2×C13#302211yescharacteristic
419C24—21no—
420#41—82no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—22no—
426C2×Q8—42no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—41no—
430C2×Q8—82no—
431C2×Q8C2×D4×C1311yescharacteristic
432C2×Q8C2×D4×C1312yes—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4C2×D4×C1311yescharacteristic
439C2×D4C2×D4×C1312yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4C2×D4×C1311yescharacteristic
447C22×C4C2×D4×C1311yescharacteristic
448C22×C4C2×D4×C1311yescharacteristic
449Q16—48no—
450SD16—48no—
451M16—24no—
452C2×C8—24no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C1312yes—
473C4⋊C4C2×D4×C1311yescharacteristic
474C4⋊C4C2×D4×C1312yes—
475C4⋊C4C2×D4×C1311yescharacteristic
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C42—22no—
492C42—22no—
493C42—21no—
494C42C2×D4×C1311yescharacteristic
495C42C2×D4×C1311yescharacteristic
496C42C2×D4×C1311yescharacteristic
497C42C24×C1311yescharacteristic
498C13#1903311yescharacteristic, direct product factor, Sylow
499C23—22no—
500C23—21no—
501C23—42no—
502C23—81no—
503C23—81no—
504C23C13×#12011yescharacteristic
505Q8—42no—
506Q8—41no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—42no—
511Q8—81no—
512Q8—82no—
513Q8—82no—
514D4—42no—
515D4—41no—
516D4—42no—
517D4—42no—
518D4—82no—
519D4—82no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—81no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4C13×#12011yescharacteristic
537C2×C4C13×#12011yescharacteristic
538C2×C4C13×#12011yescharacteristic
539C2×C4C22×D4×C1311yescharacteristic
540C2×C4C22×D4×C1311yescharacteristic
541C2×C4C22×D4×C1311yescharacteristic
542C8—24no—
543C8—24no—
544C8—42no—
545C22—21no—
546C22—21no—
547C22—41no—
548C22—42no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—41no—
553C22—162no—
554C22C13×#45612yes—
555C22C2×C13×#12011yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—42no—
563C4—42no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—82no—
568C4C13×#45312yes—
569C2—22no—
570C2—82no—
571C2—81no—
572C2C2×C13×#45311yescharacteristic
573C2C2×C13×#45611yescharacteristic
574C2C13×#302211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3561C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C13×#3239C2semidirect
3. C13×#3165C2semidirect
4. C2×C13×#497C2semidirect
5. C13×#1661C2semidirect
6. C13×#1660C2semidirect
7. C13×#1531C2semidirect
8. C13×#1527C2semidirect
9. C13×#1524C2semidirect
28. C13×#501C22semidirect
29. C13×#501C22semidirect
34. C13×#489C22semidirect
43. C13×#330C22semidirect
44. C13×#330C22semidirect
46. C13×#329C22semidirect
132. #19033C13direct (N × H)
213. #3239C2×C13semidirect
214. #3165C2×C13semidirect
215. C2×#497C2×C13semidirect
216. #1661C2×C13semidirect
217. #1660C2×C13semidirect
218. #1531C2×C13semidirect
219. #1527C2×C13semidirect
220. #1524C2×C13semidirect
285. #501C22×C13semidirect
286. #501C22×C13semidirect
291. #489C22×C13semidirect
300. #330C22×C13semidirect
301. #330C22×C13semidirect
303. #329C22×C13semidirect
498. C13#19033direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C13×#35612
C13×#32392
C13×#31652
C2×C13×#4972
C13×#16612
C13×#16602
C13×#15312
C13×#15272
C13×#15242
#1903313